30^2 + 15^2 = c^2
Use pythagorean theorem

If f(5) = 11, f ′ is cοntinuοus, and 6 5 f ′(x) dx = 19, then f(6) = 30.

Tο find the value οf f(6), we can use the Fundamental Theοrem οf Calculus. Accοrding tο the theοrem, if f(x) is cοntinuοus οn an interval [a, b] and F(x) is an antiderivative οf f(x) οn that interval, then the definite integral οf f(x) frοm a tο b is equal tο F(b) - F(a).

Given that f'(x) is cοntinuοus, we can apply the theοrem tο the integral:

∫₅₆ f'(x) dx = f(6) - f(5)

We are given that ∫₅₆ f'(x) dx = 19, and f(5) = 11. Plugging in these values, we have:

19 = f(6) - 11

Tο sοlve fοr f(6), we add 11 tο bοth sides:

f(6) = 19 + 11

f(6) = 30

Therefοre, the value οf f(6) is 30.

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The given differential equation is not exact. To determine if a differential equation is exact, we need to check if its partial derivatives satisfy a specific condition.

In this case, the given equation is dy/dx = 9xe^x – y + 6x^2. Let's find the partial derivatives of the expression on the right-hand side with respect to y and x.∂/∂y (9xe^x – y + 6x^2) = -1∂/∂x (9xe^x – y + 6x^2) = 9e^x + 12x

The condition for exactness is that these partial derivatives are equal: ∂/∂y (∂/∂x) = ∂/∂x (∂/∂y). However, in this case, we have -1 ≠ 9e^x + 12x, which means the equation is not exact.As the equation is not exact, we cannot directly solve it by finding a potential function. Other methods, such as using integrating factors or applying specific techniques for solving non-exact equations, may be required.

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Answer:

12 feet

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Given

x² - 9x + 18 = 0 ← in standard form

(x - 3)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 6 = 0 ⇒ x = 6

solution is x = 3, x = 6 → B

Answer & Explanation:

Gross income is the total pay you earn before any reduction and adjustments (taxes, mortgage, etc.).

Net income is the amount of pay you get after taxes and other reductions are taken out of your gross income; it's the money that you "actually get to take home in your pocket with" on the payday.

Answer:

-13

Step-by-step explanation:

−2+3(1−4)−2

=−2+(3)(−3)−2

=−2+−9−2

=−11−2

=−13

hope it helped

please mark me as brainliest.

Answer:

Q7  0.2

Q8  0.17

Step-by-step explanation:

Probability is the ratio of the number of possible outcome to the number of total outcome. The probability that an event will happen when added to the probability that it will not happen is 1

Given that the probability that the bulb will grow is 0.8, the probability it would not grow

= 1 - 0.8

= 0.2

A match may be won lost or drawn

Given that the probability of a win is 0.28 and that of a draw is 0.55, the probability of  a loss

= 1 - (0.28 + 0.55)

= 0.17

Answer:

100

Step-by-step explanation:

Add all of the inches together including the parts you don't see.

one side is 9 inches. there are 8 sides. so 9x8. One side in the box is 7 inches. there are 4 sides. so 7x4.  9x8 + 7x4 is equal to 72 + 28.

72 + 28=100

Answer:

this is not a right triangle

Step-by-step explanation:

^  = squared

The formula forthe Pythagorean theorem is    a^+ b^   = c^

If this is a right triangle this must be true

6^ +    8^   =   14^

36 + 64 =  196

100  is not equal to 196

So this is not a right triangle

Answer:

43.5

divide 174 ÷ 4 and you get 43.5

The correlation coefficient for the data is 0.794.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient of 0.794 indicates a strong positive correlation between weekly income and weekly grocery expenditures.

A correlation coefficient value of 0.794 suggests that as the weekly income increases, the weekly grocery expenditures tend to increase as well. The positive correlation implies that shoppers with higher incomes tend to spend more on groceries.

It is important to note that correlation does not imply causation. The study observed a correlation between income and grocery expenditures, but it does not necessarily mean that higher income directly causes shoppers to spend more on groceries. Other factors and variables may also influence grocery spending habits.

In summary, based on the given data, there is a strong positive correlation (0.794) between weekly income and weekly grocery expenditures for the surveyed shoppers.

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Answer:

The answer is 175

Answer:

Length=45 inches, width=15 inches

Step-by-step explanation:

Length=3w

Width=w

Can be written as 3w+w+3w+w

Combine like terms to get 8w

120/8=15

w=15

Width=15 inches

Length=3(15)=45

Length=45 inches

Answer:

y1=4

x2=7

y2=-3

The probability of a vanilla taffy is given as follows:

P(vanilla) = 0.31.

Hence the probability of a vanilla or banana taffy is given as follows:

P(vanilla or banana) = 0.52.

The two parameters that are needed to calculate a probability are listed as follows:

Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.

When we are given the relative frequencies, we must simply identify the desired outcomes, as follows:

Hence the probability is given as follows:

P(vanilla or banana) = P(vanilla) + P(banana) = 0.52.

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Given the function h(x) = e-3x  and we have to evaluate the function at the indicated values. So, we need to substitute the values in the given function and find the value of the function at the given points as shown below: h(13) = e-3(13)h(13) = e-39h(13) = 0.000027323h(1.5) = e-3(1.5)h(1.5) = e-4.5h(1.5) = 0.01111h(-1) = e-3(-1)h(-1) = e3h(-1) = 20.08554h(-π) = e-3(-π)h(-π) = e3πh(-π) = 23.14069.

(a) For, h(-1):

Plug x = -1 into the function:

h(-1) = e^(-3*-1)

Using a calculator, we find that h(-1) ≈ 20.086.

Similarly,

(b) For, h(-π):

Plug x = -π into the function:

h(-π) = e^(-3*-π)

Using a calculator, we find that h(-π) ≈ 23.141.

So, the value of h(x) at the given values are : h(13) = 0.000027323, h(1.5) = 0.01111, h(-1) = 20.08554 and h(-π) = 23.14069.

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Answer:

im guessing 6 is your base and your height is 15 3/4.

Formula of a triangle we must remember:

BH x 1/2 (basically dividing by 2)

94.5 (fraction form will be: 94 1/2)

94.5 divided by 2 = 47.25 <---------- decimal form

94 1/2 divided by 2 = 47 1/4 <------- fraction form

Hey!

A = $4,785.00

I = A - P = $435.00

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 2%/100 = 0.02 per year.

Solving our equation:

A = 4350(1 + (0.02 × 5)) = 4785

A = $4,785.00

The total amount accrued, principal plus interest, from simple interest on a principal of $4,350.00 at a rate of 2% per year for 5 years is $4,785.00.

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Hope you have a great day and this helped in some way <33

Answer:

this just confused me so much

Step-by-step explanation:

ooooooooooooooooooo

Answer:

Step-by-step explanation:

That Would be 43/3

Answer: 52 1/2 inches. Draw a vertical line up from the 20 week marker and where that line intersects the slanted red line and. Then take a straight edge and draw a line parallel to the "week" line on the bottom of the graph from the intersection to intersect the height line. Where the second line crosses the height line that number is the height of the plant at 20 weeks.

Answer:

20 x 4 = 60

Step-by-step explanation:

because it's says how many

Answer:

18 maybe

Step-by-step explanation:

it's either 20,19,or 18

but the secretary is the third to be elected so the answer is 18 maybe and if that doesn't work try one of the others trust me it's one of them.

hope this helps

The solution of the given differential equation using the Laplace transform is y(t) =  1 −  [tex]e^{2t}[/tex] + 2 [tex]e^{-t}[/tex].

Given differential equation is y″−2y = eˣ, y(0) = 0, y′(0) = 0. We will solve it using Laplace transforms.

To solve the given differential equation using the Laplace transform, take the Laplace transform of each term of the differential equation. Then solve for Y(s) and find y(t) by taking the inverse Laplace transform.

Here, we take L{y} for Y(s) and L{y''} and L{y'} for s²Y(s) and sY(s) respectively.

L[y′′] − 2L[y] = L[eˣ] s²Y(s) − s⋅y(0) − y′(0) − 2Y(s)

= 1s − 1.0 − 0 − 2Y(s)

= 1s − 1 

We have to rearrange the terms of the above equation in order to get Y(s) on one side.

Y(s) = 1s(s−2)(s−1) = As+Bs−2+Cs−1.

Using partial fraction expansion, A=1, B=1, and C=−2.

So,Y(s) = 1s+(1s−2)−2s−1.

We can write Y(s) as follows.Y(s) = 1s−(1s−2)+2s−1.

Then find the inverse Laplace transform of Y(s) to get the solution y(t).

y(t) = L − 1{Y(s)} = L − 1{1s} − L − 1{1s−2} + L − 1{2s−1}

= 1 −  [tex]e^{2t}[/tex] + 2 [tex]e^{-t}[/tex].

Therefore, the solution of the given differential equation using Laplace transform is y(t) =  1 −  [tex]e^{2t}[/tex] + 2 [tex]e^{-t}[/tex].

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Answer: [tex]4\times 3.5\ ft^2[/tex]

Step-by-step explanation:

Given

area of the rectangle is [tex]A=14\ ft^2[/tex]

Suppose width is given by w

So, length is [tex]l=2w-3[/tex]

The area of a rectangle is [tex]A=l\times w[/tex]

putting values

[tex]\Rightarrow A=(2w-3)w\\\Rightarrow 14=2w^2-3w\\\Rightarrow 2w^2-3w-14=0\\\Rightarrow 2w^2-7w+4w-14=0\\\Rightarrow w(2w-7)+2(2w-7)=0\\\Rightarrow (2w-7)(w+2)=0\\\\\Rightarrow w=\dfrac{7}{2}\ ft[/tex]

length is [tex]l=4\ ft[/tex]

Answer:

523.33 in^3

Step-by-step explanation:

A sphere is a 3-dimensional version of a circle. An example of a sphere is a ball

Volume of a sphere = [tex]\frac{4}{3}[/tex]π[tex]r^{3}[/tex]

Where

π = 3.14

r = radius

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

diameter = 2r

Radius = 10 in / 2 = 5 inches

[tex]\frac{4}{3}[/tex] × 3.14 ×[tex]5^{3}[/tex] = 523.33 [tex]in^{3}[/tex]

The  mass of the rod is 15.9 grams.

To find the mass of the rod, we need to integrate the linear density function over the entire length of the rod. The linear density function is given by λ = 50.0 + 20.0x, where x is the distance from one end measured in meters.

The mass of an infinitesimally small element of length dx is given by dm = λ*dx. Substituting the linear density function, we have dm = (50.0 + 20.0x)*dx.

Integrating both sides from x = 0 to x = 0.3 meters (corresponding to the length of the rod), we get:

∫dm = ∫(50.0 + 20.0x)dx
m = ∫(50.0 + 20.0x)dx
m = [50.0x + 10.0x^2] evaluated from x = 0 to x = 0.3
m = 50.00.3 + 10.0(0.3)^2
m = 15.0 + 0.9
m = 15.9 grams.

Therefore, the mass of the rod is 15.9 grams.

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Answer:

Step-by-step explanation:

If you have $2250 as against an inflation rate of 2% every year, this then means that after the first year, the value of your money becomes

2250 * 2% =

2250 * 0.02 = 45

2250 - 45 = $2205

At the end second year

$2205 * 2% =

$2205 * 0.02 = 44.1

$2205 - 44.1 = 2160.9

At end of the third year

$2160.9 - 2% =

$2160.9 * 0.02 = 43.218

$2117.682

And so on, and so forth

Answer:

x - 12 = 20

Step-by-step explanation:

If I'm wrong do x = 12 - 20